Signal processing device and method, signal processing program, and recording medium where the program is recorded

ABSTRACT

A signal processing device which outputs a discrete signal composed of a string of the sampling values and parameters m signal. The signal processing device includes a sampling circuit which samples an input signal and outputs a discrete signal, multiple function generators which generate multiple sampling functions with parameters m different from each other, plural inner product operating units for each of parameters m that take an inner product between the input signal and each of plural sampling functions and output an inner product operating value, and a judging unit which determines parameter m providing a minimum error out of multiple errors composed of differences between the sampling value and inner product operating values output from the multiple inner product operating units and outputs the parameters m signal.

The present application is a divisional application of application Ser.No. 10/591,469, filed Jul. 20, 2007, the contents of which areincorporated herein by reference.

TECHNICAL FIELD

The present invention relates to a signal processing device and a signalprocessing method for generating discrete signals by using sampling fromsignals which change in time such as video (moving picture), image, andaudio signals or those used for measurement and control. Moreover, theinvention relates to a technology of reproducing the original signalsfrom the discrete signals of images such as text, diagrams, photos andprintouts, video including moving pictures, audio, measurement results,and the like. Specifically, the invention concerns a signal processingdevice and a signal processing method for extracting changing pointswhere signal state change.

BACKGROUND ART

Recently, the digital signal technology has advanced in various fieldstargeted for videos (moving pictures), images, or audios such as fieldsof communication, broadcasting, recording media including CDs (CompactDiscs) and DVDs (Digital Versatile Discs), medical images, and printing.These fields have remarkably developed as multimedia industries or IT(Information Technology). Compressing coding to decrease the amount ofinformation performs a role of the digital signal technology for videos,images, and audios. The signal theory representatively includes theShannon's sampling theorem and, what is newer, the wavelet transformtheory (see non-patent document 1) and the like. While music CDs use thelinear PCM (Pulse Code Modulation) without compression, for example, thesignal theory to be applied is also the Shannon's sampling theorem.

There is disclosed the apparatus (e.g., see patent document 1) to createlarge display objects such as signboards, posters, banners, and thelike. For example, the apparatus create the large display objects bymaking original graphics data, the original graphics being such as text,diagrams, and the like drawn on A4-size sheets of paper, and outputtingthe data of the original graphics onto printers, cutting plotters, andthe like.

Further, patent document 2 discloses the data processing method asfollows. The method generates multiple discrete data strings based onmultiple functions categorized by differentiatable times. The methodperforms correlative calculation between input data and the multiplediscrete data strings. Based on a correlative calculation result, themethod finds a peculiar point contained in the input data to specify aclass (m) to which the object signals belong.

Non-patent document 1: The Institute of Electronics, Information andCommunication Engineers, ed. “ENCYCLOPEDIA Electronics, Information andCommunication Handbook” published by Ohmsha, Ltd., the fourth group, pp.394-396 and p. 415.

Patent document 1: Japanese Patent Laid-open No. H07-239679

Patent document 2: Japanese Patent Laid-open No. 2001-51979

DISCLOSURE OF INVENTION

Like compression coding or non-compression coding as mentioned above,there is a system that converts an input signal into a digital signaland then reproduces the original analog signal. Such system can begeneralized as an A-D/D-A conversion system. A well-known A-D/D-Aconversion system based on the Shannon's sampling theorem handlessignals whose bands are limited by the Nyquist frequency. In this case,the D-A conversion uses a function (regular function) to reproducesignals within a limited band for reproduction of sampled discretesignals to continuous waves.

One of the inventors found that a fluency function can be used tocategorize various properties of signals such as videos (movingpictures), images such as text, diagrams and natural pictures, or audiosand the like. According to this theory, the regular function based onthe Shannon's sampling theorem is one of fluency functions and remainsto be applied to one of various properties of signals. When signals withvarious properties are handled with only the regular function based onthe Shannon's sampling theorem, there may be a possibility of limitingthe quality of reproduction signals after the D-A conversion.

The above-mentioned wavelet transformation theory is for representingsignals using a mother wavelet that decomposes an object by resolution.However, the signals are not always provided with an optimum motherwavelet. Again, there may be a possibility of limiting the quality ofreproduction signals after the D-A conversion.

The fluency function is categorized by parameter m (where m is apositive integer from 1 to ∞). In parameter m, m denotes that thefunction is continuously differentiable only as Often as (m−2) times.Since the above-mentioned regular function is differentiable at anynumber of times, m is set to ∞. Further, the fluency function iscomposed of functions of degree (m−1). Particularly, a fluency DAfunction of fluency functions is given a numeric value at the k-thtargeted sampling point kτ, where τ is a sampling interval. The fluencyDA function becomes 0 at the other sampling points.

All signal properties can be classified by the fluency function havingparameter m and can be categorized into classes by parameter m.Accordingly, the fluency information theory using fluency functionsincludes the Shannon's sampling theorem, the wavelet transformationtheory, and the like that represent only part of signal properties asconventionally practiced. And, the fluency information theory ispositioned as a theoretical system representing the whole of signals. Itis expected that the use of such functions allows the D-A conversion toyield unexceptionally high-quality reproduction signals whose bands arenot limited by the Shannon's sampling theorem.

The data processing method as described in patent document 2 finds apeculiar point as a result of the correlative calculation to specifyclass m. However, the correlative calculation is time-consuming and isdisadvantageous to fast processing. Accordingly, there has been notrealized a signal processing device that effectively generates discretesignals from a continuous waveform signal based on the fluencyinformation theory. When the continuous waveform signal is an analogsignal and the discrete signal is output as a digital signal, the signalprocessing device functions as an A-D converter.

The device disclosed in patent document 1 that transforms originalimages into data broadly comprises a structure to extract outlines oftext and diagrams, a structure to extract joints and their positionsfrom curvature data, a structure to approximate the outlines usingfunctions (lines, arcs, and piecewise polynomials), a device to storecoordinate data of the joint and approximate function data, and astructure to reproduce the outlines from the stored data.

Changing points where an outline changes include joints as joining of aline or a curve. The outline largely changes at a portion near suchjoints. Accordingly, such portion is not represented by lines or arcs,but free curves, i.e., piecewise polynomials. The joints are found as apoint with a large curvature given by the piecewise polynomials. Thejoint causes an angle to largely change at a minute portion, i.e.,causes a differential coefficient to largely change. Differentialprocessing is used to extract joints that are found as points with largecurvatures.

An image is reproduced by drawing lines or curves between the changingpoints including joints using the above-mentioned approximate functions.Accordingly, correctly extracting changing points is important foraccurate reproduction.

When a scanner is used to read original images of text and diagrams, forexample, an outline is inevitably subject to jaggy or rough portions tosome extent due to a sensor noise, scanner resolutions, and the like.The jaggy or rough portions result from superposing noises which includea lot of fine and high-frequency components on the original image. Whenthe differential processing is used to find changing points includingjoints, the jaggy or rough may deviate positions for extracting changingpoints, or may be incorrectly extracted as changing points. There may bea possibility of failing to acquire accurate changing points.

This problem will be described in more detail with respect to text,diagrams, images, and videos (hereafter generically referred to asimages). A continuously changing signal may often change sharply orstepwise. Such signal changing point is corresponding to an informationchanging points (switching points or peculiar point) where signalproperties or characteristics change.

In case of image information, one screen or area contains many smallimages. When the image is processed, it is divided into minute areas(referred to as pixels) horizontally and vertically at a specifiedinterval. The image is processed in such a manner as recognizing,enlarging, transforming, and synthesizing areas (small image domains)composed of the same information in units of pixels. When small imagedomains are recognized, it becomes a subject to detect domain ends(edges). A conventional method has been used to recognize a point whereinformation about colors or brightness remarkably changes (a differenceor a differential value greatly changes) as a changing point. Thechanging point corresponds to a switching point or a peculiar point ofinformation to be described later. When differences or differentialvalues of data are used for the changing point detection, however, thereis a defect that noise may occur to change the image information andcause incorrect recognition. In addition, an image is enlarged in unitsof pixels. When an image is enlarged n times horizontally andvertically, for example, pixel information of an area of n2 becomes thesame information. Consequently, the image is subject to stepwise changesin both small area's outlines and the inside color information.

To solve the above-mentioned problems, there is proposed a method ofprocessing signal strings based on the function approximation. In thiscase, it is important to accurately recognize an information range ofthe same property, i.e., the length of a continuous signal and a smallarea domain (image outline). A method of extracting end points of thesignal length and the domain outline is compliant with conventionalmethods of using data differences, differential signals, colordifferences, and luminance differences concerning the storedinformation, i.e., methods included in the differential processing.

As mentioned above, the fluency function can be used to classify variousproperties of signals electrically acquired from images such as text,diagrams, and natural pictures, videos, or audios. Furthermore, one ofthe inventors found that the processing for this classification can beused to find changing points without using the differential processing.When a discrete signal is generated from a continuous waveform signalbased on the fluency information theory, for example, theabove-mentioned changing point can be acquired during that processingwithout using the differentiation, as will be described later. However,there has been not realized such signal processing device that cangenerate the changing points.

The function for acquiring a discrete signal from a continuous waveformsignal based on the fluency information theory is theoreticallydeveloped in detail and is defined as a sampling function in thisdescription, as will be described later. The sampling function may bereferred to as a fluency AD function. The function for acquiring acontinuous waveform signal from a discrete signal is defined as aninverse sampling function in this description. The inverse samplingfunction may be referred to as a fluency DA function. The samplingfunction and the inverse sampling function defined as such maintain theorthogonal with each other and are expressed through the use ofparameter m.

Let us suppose that a signal system acquires a discrete signal from acontinuous waveform signal based on the fluency information theory andthen acquires a continuous waveform signal from the acquired discretesignal. In order for such signal system to function, parameter m needsto be recognized at a side that acquires the continuous waveform signal.(For example, there may be an A-D/D-A conversion system that AD-convertsan analog signal based on the fluency information theory and DA-convertsthe acquired digital signal. In order for the A-D/D-A conversion systemto function, parameter m needs to be recognized at the D-A conversionside.)

This parameter m is found as follows. As will be described later, asignal processing (e.g., A-D conversion) for acquiring discrete signalstakes an inner product between an input signal of continuous waveformand the sampling function to acquire a discrete signal as a samplingvalue string. At this time, parameter m represents an input signalproperty and is assumed to be l (el). When parameter l differs fromparameter m (assumed to be m₀) for the sampling function, the innerproduct operating value resulting from the inner product differs from asampling value for the input signal at the sampling point. An erroroccurs between both. When the value m₀ in which this error may becomezero (actually, it becomes the minimum), selecting such m₀ causes l=m₀.Accordingly it becomes possible to determine parameter m from a signalthat is unknown in l.

The value of m₀ together with the discrete signal as a sampling valuestring (or the discrete signal composed of a string of inner productoperating values with the determined parameter m) may be transmitted tothe signal processing side (e.g., the D-A conversion side) to acquirecontinuous waveform signals. This signifies a signal processing (e.g., aD-A conversion) using the inverse sampling function with parameter m₀ toeasily reproduce a high-quality continuous waveform signal almost equalto the input signal.

The following outlines a representative embodiment of the inventiondisclosed in this application.

A signal processing device comprises a sampling circuit that samples aninput signal and outputs a discrete signal composed of a string ofsampling values, a plurality of function generators that generatesampling functions with parameters m different from each other; aplurality of inner product operating units for each of parameters m thattake an inner product between the input signal and the sampling functionand output an inner product operating value, and a judging unit thatdetermines parameter m providing a minimum error out of a plurality oferrors derived from differences between the sampling value and innerproduct operating values output from the plurality of inner productoperating units and outputs the parameter m signal, wherein a discretesignal composed of a string of the sampling values and the parameter msignal are outputted.

It is assumed that a signal processing generates a continuous waveformsignal from a discrete signal acquired by the signal processing deviceaccording to the invention. During such signal processing, the parameterm signal may be used to select an inverse sampling function with theparameter m. In this manner, it is possible to generate a continuouswaveform signal using the inverse sampling function with parameter mcorresponding to the parameter m to which the discrete signal belongs.That is, the invention makes it possible to easily acquire a signal toreproduce a high-quality continuous waveform signal free from limitationon bands according to the Shannon's sampling theorem.

The following outlines another representative embodiment of theinvention disclosed in this application.

A signal processing device comprises a plurality of function generatorsthat generate inverse sampling functions with parameters m differentfrom each other, when input signals include a discrete signal for anoriginal signal belonging to parameter m₀ of the parameters m and aparameter m signal indicating the parameter m₀, a function selector thatuses the parameter m signal of the input signals to select an inversesampling function with the parameter m₀ out of the inverse samplingfunctions, and a convoluting integrator that performs convolutionintegration between the discrete signal and the selected inversesampling function with parameter m₀ to acquire a continuous waveformsignal.

The signal processing device according to the invention uses theparameter m signal to notify parameter m₀ to which a discrete signalbelongs. It is possible to acquire a continuous waveform signal by usingthe inverse sampling function corresponding to a fluency signal space(to be described) to which the discrete signal belongs. That is, theinvention makes it possible to easily reproduce a high-qualitycontinuous waveform signal free from limitation on bands according tothe Shannon's sampling theorem.

During a processing to determine the parameter m, a changing pointbelongs to points where parameter m cannot be specified. Pointsincapable of specifying parameter m are broadly classified into a pointwhere no differentiation is possible (including points where a signalbecomes discontinuous), and a point where a signal is continuous and thedifferentiation is possible but parameter m changes before or after thatpoint. The former includes a point before or after which parameter mdoes not change. Such point is exemplified by a polygonal line's joiningwith m=2. The point before or after which parameter m changes isgenerically referred to as a class switching point. The point where nodifferentiation is possible is generically referred to as a peculiarpoint. (The point functioning as a class switching point and a peculiarpoint is referred to as an ultra peculiar point.)

When the image is text and a diagram in the XY coordinate system and anoutline is found, for example, let us find x and y coordinates of eachpoint on the outline that is divided into small spans. When the smallspan is assumed to be an intermediate variable, following result can beobtained. The resulting outline locus contains x coordinates of eachpoint in the coordinate system composed of X as the ordinate and thesmall span as the abscissa. The resulting outline locus contains ycoordinates of the points in the coordinate system composed of Y as theordinate and the small span as the abscissa.

These two loci are also handled based on the fluency information theory.That is, a continuous waveform signal is assumed to be the locus. Adomain is composed of multiple small spans whose separating points areassumed to be sampling points. Each sampling point has x and ycoordinates that are assumed to be sampling values. Under theseconditions, the sampling function is used to detect a changing point,i.e., a point where parameter m cannot be specified. The domain composedof multiple small spans is equivalent to a sampling interval. Thedetection provides the targeted changing point. Accordingly, when thereis given an approximate function representing the outline, the image ishighly accurately reproduced by drawing a line or a curve between thedetected changing points using the approximate function.

As mentioned above, on the assumption that there is given theapproximate function representing the outline, the invention is appliedto the signal processing device and the signal processing method foroutputting signals representing changing points. Further, on theassumption that the reproduction uses the inverse sampling function, theinvention is applied to the signal processing device and the signalprocessing method for outputting signals representing changing pointsand parameter m and discrete signals.

The following outlines still another representative embodiment of theinvention disclosed in this application. That is, a signal processingdevice comprises a sampling circuit that samples an input signal toacquire a sampling value, a plurality of function generators thatgenerate sampling functions with parameters m different from each other,and a plurality of inner product operating units for each of parametersm that take an inner product between the input signal and the samplingfunction and output an inner product operating value, wherein, whenthere is a point at which a plurality of differences between thesampling value and inner product operating values output from theplurality of inner product operating units exceeds a specified thresholdvalue with respect to any parameters m, the signal processing devicedetermines the point to be a changing point and outputs a changing pointsignal indicating the changing point.

Still another signal processing device comprises a sampling circuit thatsamples an input signal and outputs a discrete signal composed of astring of sampling values, a plurality of function generators thatgenerate sampling functions with parameters m different from each other,a plurality of inner product operating units for each of parameters mthat take an inner product between the input signal and the samplingfunction and output an inner product operating value, a class judgingunit that determines parameter m providing a minimum error out of aplurality of errors derived from differences between the sampling valueand inner product operating values output from the plurality of innerproduct operating units and outputs the parameter m signal, and whenthere is a point at which the difference exceeds a specified thresholdvalue with respect to any parameters m, a changing point judging unitthat determines the point to be a changing point and outputs a changingpoint signal indicating the changing point, wherein a combination of thediscrete signal, the parameter m signal, and the changing point signalare outputted.

As mentioned above, the changing point signal is found based on an innerproduct operation. The inner product operation uses the integration toprocess signals and can provide changing points without differentiation.This makes it possible to solve incorrect recognition of changing pointsdue to noise and problems unsolvable on moving pictures. That is, theintegration is used to process signals, making it possible to decreaseeffects of noise signals and highly accurately detect signal changes.Accordingly, it is possible to solve the problems of the prior art andmore reliably detect signal changing points and the other points whereinformation characteristics change.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a configuration diagram showing a first embodiment of a signalprocessing device according to the invention;

FIG. 2 is a graph exemplifying the sampling function with m=2;

FIG. 3 is a graph exemplifying the sampling function with m=3;

FIG. 4 is a configuration diagram showing a second embodiment of theinvention;

FIG. 5 is a configuration diagram showing a third embodiment of theinvention;

FIG. 6 is a configuration diagram showing a fourth embodiment of theinvention;

FIG. 7 diagrammatically shows classification of signals according tocontinuous differentiability;

FIG. 8 is a flowchart showing a processing to specify a class to which asignal belongs;

FIG. 9 is a configuration diagram showing an inner product operatingunit in FIG. 1;

FIG. 10 is a first diagram showing a class switching point;

FIG. 11 is a second diagram showing a class switching point;

FIG. 12 is a third diagram showing a class switching point;

FIG. 13 is a fourth diagram showing a class switching point;

FIG. 14 is a flowchart showing a processing to detect a class switchingpoint;

FIG. 15 is a configuration diagram showing a fifth embodiment of theinvention;

FIG. 16 is a configuration diagram exemplifying a convolutingintegrator;

FIG. 17 is a graph exemplifying the sampling function with m=2;

FIG. 18 is a graph exemplifying the sampling function with m=3;

FIG. 19 is a configuration diagram showing a sixth embodiment of theinvention;

FIG. 20 is a configuration diagram showing a seventh embodiment of theinvention;

FIG. 21 is a configuration diagram showing an eighth embodiment of theinvention;

FIG. 22 is a configuration diagram showing a ninth embodiment of theinvention;

FIG. 23 is a configuration diagram showing a tenth embodiment of theinvention;

FIG. 24 is another configuration diagram showing the tenth embodiment ofthe invention;

FIG. 25 is still another configuration diagram showing the tenthembodiment of the invention;

FIG. 26 is a first diagram showing a class switching point;

FIG. 27 is a second diagram showing a class switching point;

FIG. 28 is a third diagram showing a class switching point;

FIG. 29 is a first diagram showing a peculiar point;

FIG. 30 is a second diagram showing a peculiar point;

FIG. 31 is a third diagram showing a peculiar point;

FIG. 32 shows detection of a changing point;

FIG. 33 is a flowchart showing a processing to detect a changing point;

FIG. 34 is a configuration diagram showing an example of the signalprocessing device for acquiring a continuous waveform signal from adiscrete signal; and

FIG. 35 is a configuration diagram showing another example of the signalprocessing device for acquiring a continuous waveform signal from adiscrete signal.

BEST MODE FOR CARRYING OUT THE INVENTION

With reference to the diagrammed embodiments, the following describes infurther detail a signal processing device and method, a signalprocessing program, and a recording medium where the program is recordedaccording to the invention. Throughout all the drawings used to show theembodiments, the same reference numerals depict the same components orequivalents.

FIG. 1 shows a first embodiment of a signal processing device accordingto the invention. The signal processing device uses the samplingfunction to acquire a discrete signal from a continuous waveform signalbased on the fluency information theory. The embodiment aims at videosand images, and parameter m is set to three types 2, 3, and ∞. This isbecause an analysis result shows that three parameters m=2, 3, and ∞cover almost all signal properties of signals acquired from videos andimages. The invention is not limited to these three parameters.Obviously, it may be preferable to choose four parameters, i.e., m=1, 2,3, and ∞, for example, when diagrams are also included.

According to the embodiment, the digital signal processing generates adiscrete signal from a continuous waveform signal. For this reason, ananalog input signal is once sampled at an interval sufficiently shorterthan sampling interval ∞ and then is PCM encoded. Further, the samplingfunction with m=2 or 3 is settled within the finite span 0 to (J−1)τ,where J is the number of sampling points and (J−1)τ is the length. Aninner product is also taken for each sampling point within this range.FIGS. 2 and 3 exemplify the sampling functions with m=2 and 3,respectively. Each sampling function uses function span J=13.

The sampling function with m=∞ infinitely continues oscillation.Accordingly, the embodiment limits the span for this function to thesame span for the function with m=2 or 3. A resulting slight error isallowable. To increase the processing accuracy for m=∞, the range ofinner product can be wider than the above-mentioned one.

In FIG. 1, reference numeral 1 denotes a PCM coder (PCMCOD) to sampleand code analog input signals at an interval sufficiently shorter thansampling interval τ; 2 denotes a sampling circuit to sample the codedinput signal output from the PCM coder 1 at sampling interval τ andoutput a sampling value at sampling point kτ=t_(k); 3 denotes samplingfunction generators to generate sampling functions with m=2, 3, and ∞from top to bottom; 4 denotes an inner product operating unit tocalculate an inner product between an input signal and the samplingfunction based on span 0 to (J−1)τ and output an inner product operatingvalue; and 5 denotes a subtracter to subtract an inner product operatingvalue output by the inner product operating unit 4 from a sampling valueoutput by the sampling circuit 2 and output a difference. A file device(not shown) previously stores sampling functions with m=2, 3, and so thesampling function generator 3 outputs. The functions are read each timean inner product is operated.

An error operation is performed to the above-mentioned difference, andthen comparison to the results of the error operation is performed todetermine parameter m. The error operation uses a sum of squares or anarithmetic sum of absolute values for the differences depending on inputsignal properties. A sum operation is applied to errors at each samplingpoint (t_(k), t_(k+1), . . . , and t_(k+(N−2))) within the span 0 to(N−1)τ. Another available error operation may select an absolute valuefor the maximum difference in an operation span. The operation span isrepresented by N. Relatively large values are selected for N when astill picture is used as an input signal and is processed offline. Smallvalues including N=1 are selected for N when a moving picture is used asan input signal and is processed on a real-time basis. This is becauseparameter m needs to be determined fast. In this manner, any values areselected for N depending on signal properties. In the case of N=1, nosum is performed and the comparison is performed at the sampling pointsto determine parameters m.

Further, in FIG. 1, reference numeral 7 denotes an error operating unitto perform the above-mentioned error operation for differences at eachof the sampling points within the span 0 to (N−1)τ; and 8 denotes aclass judging unit that has a comparator, compares error operationresults concerning parameters m=2, 3, and ∞ from the error operatingunit 7 to detect the minimum parameter, and outputs a parameter m signalindicating that parameter m. Reference numeral 6 denotes memory foradjusting a time delay due to processing by the error operating unit 7and the class judging unit 8 with reference to sampling values outputfrom the sampling circuit 2.

The sampling circuit 2 outputs a sampling value at every samplinginterval τ to form a string of sampling values that then result in adiscrete signal. In FIG. 1, reference numeral 9 denotes an outputcircuit that combines the discrete signal with the parameter m signal toform and output a digital output signal. The combination is performed bypacketizing the discrete signal and placing the parameter m signal inthe discrete signal's header, for example. The parameter m signal onlyneeds to be capable of identifying one of three parameters m=2, 3, and ∞and therefore can be represented using a 2-bit code, for example. Thediscrete signal and the parameter m signal may be output individuallyinstead of being combined with each other.

A signal at each connecting point in FIG. 1 is shown as follows.

Input signal supplied to the inner product operating unit 4: u(t)

Sampling value for the input signal: u(t_(k))

Sampling value (inner product operating value) resulting from an innerproduct operation:

^(m)û(t_(k))

Error in output from the subtracter: _(m)ε(t_(k))

Error operation value: Em

The signal processing device according to the embodiment can beconstructed as hardware using digital circuits and memory for thecorresponding components. The signal processing device can be alsoconstructed as software, i.e., a program executed on a computer. In thiscase, the signal processing device is mainly composed of: a centralprocessing unit (CPU); memory to temporarily store such as data beingoperated; and a file device to store the signal processing program,sampling functions, and the like. The signal processing program providesthe procedure for a computer to execute each processing shown in FIG. 1.The signal processing program is available as an independent programthat is stored on recording media such as CD-ROM (Compact Disc-Read OnlyMemory).

The signal processing device can also use an analog signal processing togenerate a discrete signal from a continuous waveform signal. FIG. 4shows a second embodiment of the signal processing device using suchanalog signal processing. The device components are composed of analogcircuits whose functions and operations are the same as those of thecorresponding components in FIG. 1. As an exception, the output circuit9 outputs analog output signals. In this case, the signals may becombined by inserting the parameter m signal into a blanking period ofscanning for videos or images. A PCM coder can be used to previouslyencode and digitize discrete signals and the parameter m signal to besupplied to the output circuit 9. In this case, the output circuit 9 inFIG. 1 is used to supply digital output signals.

According to the first embodiment, the inner product operating unit 4outputs an inner product operating value for parameter m determined bythe class judging unit 8. Since that parameter m matches parameter m ofthe input signal, the output inner product operating value approximatelymatches the sampling value of the sampling circuit 2. Accordingly, theinner product operating value can replace the sampling value to besupplied to the output circuit 9. In this case, a selector is providedto select an inner product operating value for the determined parameterm using the parameter m signal output from the class judging unit 8 andsupply the output circuit 9 with the selected inner product operatingvalue. FIG. 5 shows a third embodiment that provides the selector. InFIG. 5, reference numeral 10 denotes the selector. In this manner, thesignal processing device in FIG. 5 outputs a discrete signal composed ofa string of inner product operating values. As mentioned above, thesignal processing device in FIG. 1 outputs a discrete signal composed ofa string of sampling values. The inner product operating value and thesampling value each are discrete values acquired at every samplinginterval. Therefore, the discrete signals can be referred to as adiscrete value string.

According to the first embodiment, some input signals may contain aportion where parameter m suddenly changes. When such input signals areprocessed, it is effective to provide the signal processing device witha circuit to determine a class switching point where parameter msuddenly changes. The signal processing accuracy can be enhanced byreliably locating switching points for parameter m.

FIG. 6 shows a fourth embodiment of the signal processing device that isequivalent to the device in FIG. 1 provided with a class switching pointjudging unit. In FIG. 6, reference numeral 11 denotes a class switchingpoint judging unit to compare errors for m=2, 3, and ∞ from thesubtracter 5 with a predetermined threshold value. There may be a casewhere all errors exceed the threshold value and there is a change in theparameter m signal from the class judging unit 8 near the samplingpoint. In this case, the class switching point judging unit 11determines that sampling point to be a class switching point and outputsa switching point signal. The output circuit 9 is supplied with theswitching point signal as well as the discrete signal and the parameterm signal and combines these signals to generate a digital output signal.The combination is performed by packetizing the discrete signal andplacing the parameter m signal and the switching point signal in thediscrete signal's header, for example. The switching point signal onlyneeds to be capable of identifying its presence or absence and thereforecan be represented using a 1-bit code, for example. The discrete signal,the parameter m signal, and the switching point signal may beindividually output instead of being combined. The circuits other thanthe class switching point judging unit 11 and the output circuit 9 arethe same as those shown in FIG. 1.

The following theoretically describes the principle of operations andprocessing flows of the signal processing device according to the firstthrough fourth embodiments. The description to follow assumes thatparameter m is not limited to m=2, 3, and ∞ but represents multipleparameters in general.

<I> Determining an Optimum Class for an Unknown Signal in a PartialSpace of the Fluency Signal Space

The following fluency signal space is defined because the fluencyfunction expresses a signal with the length and the phase. It is firstclarified to which class of partial signal space in the fluency signalspace an unknown class signal belongs. Specifically, the class to whichthe signal belongs is determined based on a difference between thesampling value of the input signal (original signal) and a valueresulting from an inner product operation between the sampling functionsystem and the original signal.

(1) Defining the Fluency Signal Space

The signal space to be discussed hereinafter is assumed to be fluencysignal space ^(m)S(τ), where m=1, 2, . . . , and ∞, as a partial spaceof the representative Hilbert space equation (2) whose inner product isdefined by equation (1).

$\begin{matrix}{{< u},{{v >_{L\; 2}}\overset{\Delta}{=}{\int_{- \infty}^{\infty}{{u(t)}\overset{\_}{v(t)}\ {t}}}}} & (1) \\{{L_{2}(R)}\overset{\Delta}{=}\left\{ {u{{\int_{- \infty}^{\infty}{{{u(t)}}^{2}\ {t}}} < {+ \infty}}} \right\}} & (2)\end{matrix}$

Piecewise polynomials are defined by equation (3) and are continuouslydifferentiable only (m−2) times. Equation (4) defines fluency signalspace ^(m)S(τ) as a signal space, using the function system (a set offunctions)

{^(m)φ(t−kτ)}_(k=−∞) ^(∞)

composed of the piecewise polynomials of degree (m−1) as a base. Asmentioned above, τ represents a sampling interval for acquiring adiscrete signal (sampling value) from continuous signals. Each samplingpoint along the time axis is represented as t_(k) (=kτ)

$\begin{matrix}{{{\,^{m}\varphi}(t)}\overset{\Delta}{=}{\int_{- \infty}^{\infty}{\left( \frac{\sin \; \pi \; f\; \tau}{\pi \; f\; \tau} \right)^{m}^{j\; 2\; \pi \; {tt}}\ {f}}}} & (3) \\{{{\,^{m}S}(\tau)}\overset{\Delta}{=}\left\lbrack {{\,^{m}\varphi}\left( {t - {k\; \tau}} \right)} \right\rbrack_{k = {- \infty}}^{\infty}} & (4)\end{matrix}$

When parameter m is 1, fluency signal space ^(m)S(τ) is categorized as asignal space composed of the Walsh function system. When parameter m is2, fluency signal space ^(m)S(τ) is categorized as a signal spacecomposed of a polygonal lines function (polygon). When parameter m is aninfinite limit, fluency signal space ^(m)S(τ) is categorized as a rangelimit signal space composed of an infinitely continuously differentiableSinc function system (regular function system). FIG. 7 is a conceptualdiagram of these fluency signal spaces. Signals in the fluency signalspace ^(m)S(τ) are categorized according to the continuousdifferentiability.

(2) Meaning of the Sampling Function

Signal space ^(m)S(τ) is provided with a feature that can acquire thesignal's sampling value string

{u(t_(k))}_(k=−∞) ^(+∞)

by taking an inner product between a given signal u(t) belonging tomS(□) and the sampling function system belonging to mS(□). The functionhaving this feature is called a sampling function and is expressed asfollows.

_([AD]) ^(m)ψ(t)

The foregoing is expressed by equation (5) to follow.

^(∃l) _([AD]) ^(m)ψ(t)ε^(m)S,^(∀) u(t)ε^(m) S, ^(∀) kεZ,<u(t),_([AD])^(m)ψ(t−t _(k))>=u(t _(k))  (5)

In equation (5), the symbol

“∃l”

signifies the sole existence. The symbol

“∀”

signifies an arbitrary element. The symbol

“Z”

signifies a set of whole integers.

(3) Using the Sampling Function to Specify a Class of Partial SignalSpace to which an Unknown Signal Belongs

It is assumed that ^(m)u(t) represents a signal belonging to signalspace ^(m)S(τ). The following determines to which class of signals influency signal space ^(m)S(τ) an unknown class signal u(t) belongs.

When there are plural signals ¹u(t), ²u(t), . . . , ^(i)u(t), . . . ,and ^(∞)u(t), the following equation expresses a fluency signal spacefor m₀ out of plural m=1, 2, . . . , m₀, . . . , and ∞.

^(m) ⁰ S(τ)

The sampling function system belonging to this fluency signal space isexpressed as follows.

_([AD]) ^(m) ⁰ ψ(t−t_(k))

Let us take an inner product between the signals and the samplingfunction system.

(i) l=m₀, there is m₀ that satisfies relational expression (6).

^(∀) kεZ,< ^(l) u(t),_([AD]) ^(m) ⁰ ψ(t−t _(k))>=^(l) u(t _(k))  (6)

(ii) When l≠m₀, there is m₀ that satisfies relational expression (7).

^(∃) kεZ,< ^(l) u(t),_([AD]) ^(m) ⁰ ψ(t−t _(k))>≠^(l) u(t _(k))  (7)

Using this relation, the class for a given unknown class signal u(t) canbe specified as an element of the following.

^(m) ⁰ S(τ)

Referring now to FIG. 8, the following describes a processing procedureto determine the class based on the above-mentioned principle.

A signal is input (Step S1). One m₀ is selected (Step S2). The followingsampling function is defined for each of sampling points t_(k), t_(k+1),. . . , and t_(k+(J−2)) within the span 0 to (J−1)τ.

_([AD]) ^(m) ⁰ ψ(t−t_(k))

where k=k, k+1, . . . , and k+(J−2).

The processing calculates an inner product between the sampling pointand input signal u(t) for the span 0 to (J−1)τ (Step S3). Equation (8)to follow expresses the value resulting from this operation.

^(m) ⁰ û(t _(k))=<u, _(AD) ^(m) ⁰ ψ(t−t _(k))>  (8)

This is referred to as an inner product operating value.

The processing then calculates an absolute value for a differencebetween the input signal for the inner product operating value acquiredat Step S3 and sampling value u(tk) (Step S4). The absolute value isexpressed by equation (9) as follows.

_(m) ₀ ε(t _(k))=|u(t _(k))−^(m) ⁰ û(t _(k))|  (9)

The processing at Steps S2 to S4 is repeated by changing m0 (Step S5) tocalculate a difference for each m₀.

The processing calculates a sum of squares for the differences found atStep S4 for each m0 (Step S6). The calculation is expressed by equation(10) as follows.

$\begin{matrix}{E_{m_{0}} = {\sum\limits_{p = 0}^{N - 1}{{{}_{m0}^{}{}_{}^{}}\left( t_{k + p} \right)}}} & (10)\end{matrix}$

The error operation may be an arithmetic sum of absolute values for thedifferences depending on signal properties. In this case, the followingequation (11) is used.

$\begin{matrix}{E_{m_{0}} = {\sum\limits_{p = 0}^{N - 1}{{\,_{m_{0}}ɛ}\left( t_{k + p} \right)}}} & (11)\end{matrix}$

Alternatively, the error operation may select the maximum of absolutevalues for the differences. In this case, the following equation (12) isused.

E _(m) ₀ =MAX_(p=0) _(m) ₀ ^(N−1)ε(t _(k+p))  (12)

The following expresses the minimum in the sum of squares found byequation (10).

$\min\limits_{m_{0}}E_{m_{0}}$

The processing specifies m0 in this equation to be the class to whichsignal u(t) belongs (Step S7).

FIG. 9 is used to describe an example of the inner product operatingunit 4 in FIG. 1 constructed according to the above-mentioned theory.The inner product is equivalent to integrating a product between theinput signal and the sampling function within the span 0 to (J−1)τ atsampling point t=t_(k). When the time point to start the samplingfunction is selected as an origin, the time for the delayed input signalcan be aligned to the time for the sampling function by delaying theinput signal for (J−1)τ/2. The processing then operates an inner productbetween the sampling function and the delayed input signal by delayingthe sampling function for τ. This makes it possible to yield thefollowing inner product operating values corresponding to the samplingpoints t_(k), t_(k+1), . . . , and t_(k+(J−)2) at an interval of τ

^(m) ⁰ û(t_(k))

where k=k, k+1, . . . , and k+(J−2).

The processing starts generating the sampling function from the nextsampling point t_(k+(J−1)) and performs the similar operations.

As shown in FIG. 9, the inner product operating unit 4 for parameter mis composed of: a delay circuit 41 to delay input signal u(t) by(J−1)τ/2; delay circuits 42-1 through 42-(J−2) for the number of (J−2)to delay the sampling function by τ; multipliers 43-0 through 43-(J−2)for the number of (J−1) to multiply a delayed input signal by thesampling function; integrators 44-0 through 44-(J−2) for the number of(J−1) to integrate an output signal from the multiplier 43; and aswitcher 45 to switch output signals from the integrator 44 in the orderof 0 to (J−2) for output.

<II> Detecting a Class Switching Point

It is assumed that a given signal is represented by a linkage of signalshaving different classes. Such signal has points (class switchingpoints) as boundaries for the signals having different classes. An innerproduct is taken between the sampling function system and the originalsignal (input signal) to yield an inner product operating value. Theclass switching point is detected based on an error between the innerproduct operating value and the sampling value for the input signal.

(1) Defining and Classifying Class Switching Points

With reference to a given point on one signal, the original signal maybe represented by signals having different classes in the domains beforeand after that point. For example, in domain A, the signal isrepresented as a signal for class mA, i.e.,

^(m) ^(A) S

In domain B, the signal is represented as a signal for class mB, i.e.,

^(m) ^(B) S

In such case, there is a boundary linking signals having differentclasses. The boundary is called a class switching point and isrepresented as P(mA, mB). The class switching points contain a peculiarpoint (undifferentiatable point), called an ultra peculiar point.

The class switching point P(m_(A), m_(B)) is classified into twocategories according to properties at that point as follows.

(i) The point P(m_(A), m_(B)) makes the signal continuous butundifferentiatable and satisfies the condition m_(A)≠m_(B). FIG. 10exemplifies such class switching point as the ultra peculiar point.

(ii) The point P(m_(A), m_(B)) makes the signal continuous anddifferentiatable and satisfies the condition m_(A)≠m_(B). FIG. 11exemplifies such class switching point.

The point P(m_(A), m_(B)) may contain a case where m is unchanged butundifferentiatable and satisfies the condition m_(A)=m_(B)≧3. FIG. 12exemplifies such point called a peculiar point that is not a classswitching point. There may be a case where an unknown signal isrepresented as a signal belonging to the class m=1 (step) or m=2(polygonal line). The signal may contain discontinuous points andcontinuous but undifferentiatable points (connections between polygonallines) that are not targeted for detection according to the invention.

(2) Detecting a Class Switching Point

The following describes detection of a class switching point withreference to FIG. 13 (specifically detection of an ultra peculiar point)as an example. As shown in FIG. 13, it is assumed that signal u(t) isrepresented as a signal (polygon or polygonal line) belonging to theclass m=2 in a given span (domain A). Further, it is assumed that signalu(t) is represented as a signal belonging to the class m=∞ at theboundary t=tsp and in the subsequent span (domain B). Moreover, it isassumed that there is another signal class m=3.

(i) In domain A, an inner product operating value is acquired by takingan inner product between the sampling function

_([AD]) ^(m) ⁰ sψ(t)

for class m0 and signal u(t). The calculation is performed to find anerror (represented as

_(m) ₀ ε(A)

m₀=2, 3, and ε. Out of errors ₂ε(A), ₃ε(A), and _(∞)ε(A), ₂ε(A) becomesthe minimum.

(ii) Similarly, in domain B, errors ₂ε(B), ₃ε(B), and _(∞)ε(B) areacquired. Of these, _(∞)ε(B) becomes the minimum.

(iii) Errors ₂ε(t_(sp)), ₃ε(t_(sp)), and ₂₈ε(t_(sp)) are found in thevicinity of ultra peculiar point t=t_(sp) where the class switches.Values ₂ε, ₃ε, and _(∞)ε all become large, making it difficult toclearly specify a class. Based on this information, the class switchingpoint is positioned.

With reference to FIG. 14, the following describes a class determinationprocessing procedure based on the above-mentioned principle. Asmentioned above, the description concerns the example where the samplingfunction is applicable to the classes m₀=2, 3, and ∞.

At each of sampling points tk, tk+1, . . . , and tk+(J−2), theprocessing takes an inner product between input signal u(t) and thesampling function

_([AD]) ^(m) ⁰ ψ(t)

to find an inner product operating value

^(m) ⁰ û(t_(k))

where k=k, k+1, . . . , and k+(J−2). The processing then calculates anerror

_(m) ₀ ε(t_(k))

between the calculated inner product operating value and the samplingvalue u(tk) for the input signal (Step S8). So far, the processing isthe same as that at Steps S1 through S5 in FIG. 8 based on m0=2, 3, and∞.

The processing compares errors ₂ε(t_(k)), ₃ε(t_(k)), and _(∞)ε(t_(k))corresponding to m₀ with predetermined threshold value ε_(th) (Step S9).When all the errors are greater than or equal to threshold value ε_(th)(Step S10), the processing further calculates the error of points Kbefore and after t=t_(k) (Step S11). It may be determined that, in therange k−K≦n<k, the error

_(m1)ε(t_(n))

corresponding to m1 is smaller than errors for the other classes and istherefore the minimum and that, in the other range k<n≦k+K, the error

_(m2)ε(t_(n))

corresponding to m₂ ≠m₁ is smaller than errors for the other classes andis therefore the minimum (Step S12). In this case, the processingassumes the point for t=tk to be the ultra peculiar point, i.e., theclass switching point (Step S13).

When the processing determines at Step S10 that all errors are notgreater than or equal to threshold value ε_(th) and at least one erroris smaller than or equal to ε_(th), a change may be detected inparameter m0 that gives a minimum error at a given point (Step S14). Theprocessing assumes that changing point to be the class switching point.When no change is detected in parameter m0, the processing determinesthat there is no class switching point (Step S15). When the processingdetermines at Step S12 that no change is detected in parameter m0 givinga minimum error and that the condition m₂=m₁ is satisfied, theprocessing determines that there is no class switching point (Step S15).

As mentioned above, the first through third embodiments provide thesignal processing to acquire a discrete signal from the input signal asthe continuous waveform signal. The signal processing makes it possibleto clarify the class to which the input signal to be processed belongsand acquire the parameter m signal indicating the class as well as adiscrete signal (discrete value string). The fourth embodiment makes itpossible to acquire the switching point signal indicating the classswitching point corresponding to input signals.

The above-mentioned parameter m signal may be used to select the inversesampling function for parameter m in the signal processing to generate acontinuous waveform signal from a discrete signal. In this manner, thecontinuous waveform signal can be generated using the inverse samplingfunction corresponding to parameter m to which the discrete signalbelongs. Consequently, it is possible to reproduce high-qualitycontinuous waveform signals independently of band limitations accordingto the Shannon's sampling theorem.

As mentioned above, the signal processing device according to theinvention is supplied with a discrete signal acquired from a continuouswaveform signal based on the fluency information theory and generates acontinuous waveform signal from the discrete signal using the inversesampling function. The following describes the signal processing deviceaccording to the invention.

FIG. 15 shows a fifth embodiment of the signal processing deviceaccording to the invention. The signal processing device according tothis embodiment is supplied with a digital output signal output from thesignal processing device according to the first embodiment as shown inFIG. 1, for example. The digital signal processing is performed toacquire the continuous waveform signal from a discrete signal.

The inverse sampling function used for the signal processing isbiorthogonal to the above-mentioned sampling function that is used forthe signal processing device according to the first embodiment. FIGS. 17and 18 show function examples under the conditions of m=2 and 3. Theinverse sampling function with m=2 and 3 is settled within the finitespan 0 to (P−1)τ. The convoluting integration is performed at eachsampling point within this span. When m is 3, P is typically set to 5.The inverse sampling function with m=∞ infinitely continues oscillation.Accordingly, the device limits the span for this function to the samespan for the function with m=2 or 3. A resulting slight error isallowable. To increase the processing accuracy for m=∞, the range ofconvolution integration can be wider than the above-mentioned one.

In FIG. 15, reference numeral 21 denotes a signal input circuit that issupplied with a digital signal composed of a discrete signal of anoriginal signal belonging to parameter m and a parameter m signalindicating the parameter m and separates these signals from each otherand outputs them; 22 denotes an inverse sampling function generator thatgenerates an inverse sampling function for each of parameters m; 23denotes an inverse sampling function selector that selects an inversesampling function with parameter m corresponding to the discrete signalout of inverse sampling functions with each of parameters m output fromthe inverse sampling function generator 22; 24 denotes a convolutingintegrator that acquires a continuous waveform signal by performingconvolution integration between the discrete signal from the signalinput circuit 21 and the inverse sampling function selected by theinverse sampling function selector 23; and 25 denotes a PCM decoder(PCMDEC) that outputs an analog signal equivalent to the continuouswaveform signal output from the convoluting integrator 24. The inversesampling functions for m=2, 3, and ∞ output from the inverse samplingfunction generator 22 are previously stored in a data file (not shown)of a storage device and are read each time a function is selected.

Let us suppose that the inverse sampling function with parameter m isexpressed as follows.

_([DA]) ^(m)ψ(t)

As mentioned above, the inverse sampling function and the samplingfunction are associated with each other so as to be biorthogonal. Inparticular, the inverse sampling function is configured to be set to agiven value at a targeted sampling point and reset to 0 at the othersampling points.

Equation (13) to follow expresses the convolution integration for DAoperations.

$\begin{matrix}{\sum\limits_{k = {- \infty}}^{k = \infty}{{u\left( t_{k} \right)}{{\,_{\lbrack{DA}\rbrack}^{m}\psi}\left( {t - t_{k}} \right)}}} & (13)\end{matrix}$

Operating equation (13) can yield continuous waveform signal u(t) thatreproduces the original signal.

Accordingly, a sampling value for sampling point t_(k) is held for(P−1)τ from t=t_(k). The held signal is multiplied by the inversesampling function that starts being generated from t=t_(k). Theoperation is performed as often as (P−2) times put off for a samplinginterval of τ. The resulting products are added accumulatively insuccession. The same operation is repeated from the next sampling pointt_(k+(P−1)) to operate the convolution integration and acquirecontinuous waveform signal u(t). Such processing to acquire a continuouswaveform signal from discrete signals smoothly connects between each ofdiscrete values using the DA function (inverse sampling function) withparameter m. The processing can be defined as an interpolation or aprocessing treatment to acquire a continuous signal.

In consideration for this, for example, the convoluting integrator 24 inFIG. 15 can be constructed as shown in FIG. 16. That is, the convolutingintegrator 24 is composed of: delay circuits 51-1 through 51-(P−2) asmany as (P−2) to delay the inverse sampling function by τ; holdingcircuits 52-0 through 52-(P−2) as many as (P−1) to hold sampling valuesfor sampling points t_(k), t_(k+1), . . . , and t_(k+(P−2)) at intervalτ; multipliers 53-0 through 53-(P−2) as many as (P−1) to multiply aholding signal output from the holding circuit 52 by the inversesampling function; and an accumulator 54 to accumulatively add outputsignals from the multiplier 53 in the order of output.

Similarly to the first embodiment, the signal processing deviceaccording to the embodiment can be constructed as hardware using digitalcircuits and memory for the corresponding components. The signalprocessing device can be also constructed as software, i.e., a programexecuted on a computer. In this case, the signal processing device ismainly composed of: a central processing unit (CPU); memory totemporarily store data being operated; and a file device to store thesignal processing program, sampling functions, and the like. The signalprocessing program provides the procedure for a computer to execute theprocessing shown in FIG. 15. The signal processing program is availableas an independent program that is stored on recording media such asCD-ROM (Compact Disc-Read Only Memory).

As mentioned above, the embodiment enables the signal processing usingthe inverse sampling functions appropriated to classes, making itpossible to acquire high-quality reproduction signals.

The input signal according to the embodiment may be a digital signaloutput from the signal processing device according to the thirdembodiment as shown in FIG. 5. The same continuous waveform signal(reproduction signal) can be acquired.

While the embodiment disposes the PCM decoder 25 at the output side, itcan be disposed at the input side. Such construction is shown as a sixthembodiment of the invention in FIG. 19. In FIG. 19, the PCM decoder 26converts a digital discrete signal into an analog discrete signal. InFIG. 19, the inverse sampling function generator 22, the inversesampling function selector 23, and the convoluting integrator 24 havethe same functions as those shown in FIG. 15, but are constructed asanalog circuits.

FIG. 20 shows a seventh embodiment of the invention for supplying analogsignals. For example, the input signal is an analog signal output fromthe signal processing device according to the second embodiment shown inFIG. 4 and is composed of a discrete signal and a parameter m signalcombined with each other. The signal input circuit 27 in FIG. 20separates the combination of the discrete signal and the parameter msignal from each other. Similarly to the sixth embodiment, analogcircuits are used for the inverse sampling function generator 22, theinverse sampling function selector 23, and the convoluting integrator24.

FIG. 21 shows an eighth embodiment of the invention for supplying asignal composed of the discrete signal and the parameter m signalprovided with a switching point signal. The input signal is a digitalsignal output from the signal processing device according to the fourthembodiment as shown in FIG. 6, for example. The signal input circuit inFIG. 21 separates the combination of the discrete signal, the parameterm signal, and the switching point signal from each other. The inversesampling function selector 23 uses the parameter m signal and theswitching point signal as selection control signals. When the switchingpoint signal arrives, the inverse sampling function selector 23 changesthe class and uses the parameter m signal to determine parameter m forthe class to be changed. In this manner, the inverse sampling functionselector 23 selects the inverse sampling function for the determinedparameter m. The inverse sampling function 22, the convolutingintegrator 24, and the PCM decoder 25 are the same as those for thefifth embodiment.

Obviously, the PCM decoder 25 can be disposed between the input signalcircuit 21 and the convoluting integrator 24. Similarly to the sixthembodiment, analog circuits can be used for the inverse samplingfunction generator 22, the inverse sampling function selector 23, andthe convoluting integrator 24.

The signal processing devices according to the first, third, and fourthembodiments (FIGS. 1, 5, and 6) and the signal processing deviceprovided with the PCM coder at the output side according to the secondembodiment are supplied with analog continuous waveform signals andoutput digital discrete signals (discrete value strings). The signalprocessing devices according to the first, third, and fourth embodimentscan be interpreted as an AD converter. Similarly, the signal processingdevices according to the fifth, sixth, and eighth embodiments can beinterpreted as a DA converter that is supplied with a digital discretesignal and outputs an analog continuous waveform signal. When bothdevices construct an A-D/D-A conversion system, both devices may bedirectly connected or may be connected via a transmission system or arecording system. When data passes through the transmission system orthe recording system, information compression coding or transmissionpath coding may be provided to decrease the amount of data. In thiscase, data passes through the transmission system or the recordingsystem, and then is decoded and D-A converted.

When the transmission system is a communication system, it is availableas internet, cellular phone networks, and cable television, orground-based broadcasting and satellite broadcasting using radio waves.The recording system can provide recording media such as CD (CompactDisc) and DVD (Digital Versatile Disc). Through the use of thesetechnologies, it is expected to provide higher-precision video than everbefore. When it is enough to provide the same reproduction quality asbefore, it is possible to narrow the communication system's transmissionband and extend the recording time on CD and DVD.

When the A-D/D-A conversion system is applied to a print system, thesystem can provide much higher-precision images than ever before. Evenwhen an image is enlarged or reduced, it is expected to maintain highquality or provide high scalability.

FIG. 22 shows a ninth embodiment of the signal processing deviceaccording to the invention. The signal processing device according tothe embodiment determines a changing point for parameter m using thesampling function based on the fluency information theory and outputs achanging point signal indicating the changing point. The embodiment istargeted for images such as text and diagrams and uses three types ofparameters m=2, 3, and ∞. Obviously, the invention is not limited tothese three types of parameters. For example, available parameters maybe four such as m=1, 2, 3, and ∞ or may be only one such as m=2. Typesof parameters can be selected depending on targets. When only parameterm=2 is available, this signifies that a diagram is composed of onlypolygonal lines.

The embodiment assumes that there is provided an approximate functionrepresenting an outline. The digital signal processing is used to outputa signal indicating a changing point. The input signal is a digitalcontinuous waveform signal resulting from separating an outline by smallspans. The sampling function with m=2 or 3 is settled within the finitespan 0 to (J−1)τ, where J is the number of sampling points and (J−1)τ isthe length. An inner product is taken within this span at every samplingpoint. The examples in the above FIGS. 2 and 3 present the samplingfunctions with m=2 and 3 when the center of the span is used as anorigin. In both examples, the function span is J=13.

As mentioned above, the sampling function with m=∞ infinitely continuesoscillation. The embodiment limits the span for this function to thesame span for the function with m=2 or 3. A resulting slight error isallowable. To increase the processing accuracy for m=∞, the range ofinner product can be wider than the above-mentioned one.

In FIG. 22, reference numeral 2 denotes a sampling circuit to assign asampling point to each of points separating multiple small spans, samplean input signal at sampling interval τ, and output a sampling value atsampling point kτ=t_(k); 3 denotes sampling function generators togenerate sampling functions with m=2, 3, and ∞ from top to bottom; 4denotes an inner product operating unit to calculate an inner productbetween an input signal and the sampling function based on span 0 to(J−1)τ and output an inner product operating value; and 5 denotes asubtracter to subtract an inner product operating value output by theinner product operating unit 4 from a sampling value output by thesampling circuit 2 and output a difference. A file device (not shown)previously stores sampling functions with m=2, 3, and ∞ the samplingfunction generator 3 outputs. The functions are read each time an innerproduct is operated. One sampling interval approximately contains somany small spans that the input signal is assumed to be a continuouswaveform signal.

The difference is compared with a predetermined threshold value. When adifference for any parameter m exceeds the threshold value, that pointis assumed to be a changing point. In FIG. 22, reference numeral 12denotes a changing point judging unit that compares a difference foreach parameter m with the threshold value to determine a changing point.The changing point is represented by ordinal position k for thecorresponding sampling point counted from a coordinate point on theimage's XY coordinate or from the first sampling point.

The image reproduction uses the changing point information. Depending onimage properties, it may be effective to use the information aboutparameter m as well during reproduction. In such case, the class judgingunit 8 is added in FIG. 22. The class judgment, i.e., the determinationof parameter m is performed after an error operation for the difference.The error operation uses a sum of squares or an arithmetic sum ofabsolute values for the differences depending on input signalproperties. A sum operation is applied to errors at the sampling points(tk, tk+1, . . . , and tk+(N−2)) within the span 0 to (N−1)□. Anotheravailable error operation may select an absolute value for the maximumdifference in an operation span. The operation span is represented by N.Relatively large values are selected for N when a still picture is usedas an input signal and is processed offline. In FIG. 22, referencenumeral 7 denotes an error operating unit to perform the above-mentionederror operation for differences between each of the sampling pointswithin the span 0 to (N−1)τ. In FIG. 22, reference numeral 13 denotes anoutput circuit to output a changing point signal indicating the changingpoint and a parameter m signal indicating parameter m as digital outputsignals. The parameter m signal only needs to be capable of identifyingone of three parameters m=2, 3, and ∞ and therefore can be representedusing a 2-bit code.

Signals at each of the connection points in FIG. 22 include an inputsignal supplied to the inner product operating unit 4, a sampling valuefor the input signal, a sampling value resulting from the inner productoperation, an error in output from the subtracter 5, and an erroroperation value. These signals are indicated similarly to the firstembodiment.

The signal processing device according to the embodiment can beconstructed as hardware using digital circuits and memory for thecorresponding components. The signal processing device can be alsoconstructed as software, i.e., a program executed on a computer. In thiscase, the signal processing device is mainly composed of: a centralprocessing unit (CPU); memory to temporarily store such as data beingoperated; and a file device to store the signal processing program,sampling functions, and the like. The signal processing program providesthe procedure for a computer to execute each of the processing shown inFIG. 22. The signal processing program is available as an independentprogram that is stored on recording media such as CD-ROM (CompactDisc-Read Only Memory).

When one type of parameter m is available, there are available one innerproduct operating unit 4 and one sampling function generator 3 in FIG.22. The error operating unit 7 and the class judging unit 8 are omitted.

When an analog signal is used as the input signal according to theembodiment, the analog input signal is once sampled at theabove-mentioned small span and is PCM coded. In addition, when the inputsignal is an analog signal, an analog signal processing can be used toprocess signals to acquire a changing point signal. In this case, analogcircuits are used for the device components in FIG. 22.

FIG. 23 shows a tenth embodiment of the signal processing deviceaccording to the invention. The embodiment is targeted for images suchas text and diagrams and uses three types of parameters m=2, 3, and ∞.Obviously, the invention is not limited to these three types ofparameters. For example, available parameters may be four such as m=1,2, 3, and ∞ or may be only one such as m=2. Types of parameters can beselected depending on targets.

The embodiment assumes the use of the inverse sampling function toreproduce images. A digital signal processing is used to process signalsto output a signal indicating a changing point, a signal indicatingparameter m, and a discrete signal. The input signal is a digitalcontinuous waveform signal resulting from separating an outline by smallspans. The sampling functions with m=2, 3, and ∞ are the same as thoseused for the ninth embodiment.

In FIG. 23, reference numeral 2 denotes a sampling circuit to assign asampling point to each of points separating multiple small spans, samplean input signal at sampling interval τ, and output a sampling value atsampling point kτ=t_(k); 3 denotes sampling function generators togenerate sampling functions with m=2, 3, and ∞ from top to bottom; 4denotes an inner product operating unit to calculate an inner productbetween an input signal and the sampling function based on span 0 to(J−1)τ and output an inner product operating value; and 5 denotes asubtracter to subtract an inner product operating value output by theinner product operating unit 4 from a sampling value output by thesampling circuit 2 and output a difference. A file device (not shown)previously stores sampling functions with m=2, 3, and ∞ the samplingfunction generator 3 outputs. The functions are read each time an innerproduct is operated. One sampling interval approximately contains somany small spans that the input signal is assumed to be a continuouswaveform signal.

An error operation is performed for the above-mentioned difference.Parameters m are then compared to be determined. The error operationuses a sum of squares or an arithmetic sum of absolute values for thedifferences depending on input signal properties. A sum operation isapplied to errors at the sampling points (t_(k), t_(k+1), . . . , andt_(k+(N−2))) within the span 0 to (N−1)τ. Another available erroroperation may select an absolute value for the maximum difference in anoperation span. The operation span is represented by N. Relatively largevalues are selected for N when a still picture is used as an inputsignal and is processed offline.

Further, in FIG. 23, reference numeral 7 denotes an error operating unitto perform the above-mentioned error operation for differences betweeneach of the sampling points within the span 0 to (N−1)τ; and 8 denotes aclass judging unit that has a comparator, compares error operationresults concerning parameters m=2, 3, and ∞ from the error operatingunit to detect the minimum parameter, and outputs a parameter m signalindicating that parameter m. Reference numeral 6 denotes memory foradjusting a time delay due to processing by the error operating unit 7and the class judging unit 8 with reference to sampling values outputfrom the sampling circuit 2.

In FIG. 23, reference numeral 11 denotes a changing point judging unitto compare errors for m=2, 3, and ∞ from the subtracter 5 with apredetermined threshold value. There may be a case where all errorsexceed the threshold value. In this case, the changing point judgingunit 11 determines that sampling point to be a changing point andoutputs a changing point signal.

The sampling circuit 2 outputs a sampling value at every samplinginterval □ to form a string of sampling values that then result in adiscrete signal. In FIG. 23, reference numeral 9 denotes an outputcircuit that combines the discrete signal, the parameter m signal, andthe changing point signal with each other to form and output a digitaloutput signal. The combination is performed by packetizing the discretesignal and placing the parameter m signal and the switching point signalin the discrete signal's header, for example. The parameter m signalonly needs to be capable of identifying one of three parameters m=2, 3,and ∞ and therefore can be represented using a 2-bit code, for example.The switching point signal only needs to be capable of identifying itspresence or absence and therefore can be represented using a 1-bit code,for example. The discrete signal, the parameter m signal, and theswitching point signal may be output individually instead of beingcombined with each other.

The signal processing device according to the embodiment can beconstructed as hardware using digital circuits and memory for thecorresponding components. The signal processing device can be alsoconstructed as software, i.e., a program executed on a computer. In thiscase, the signal processing device is mainly composed of: a centralprocessing unit (CPU); memory to temporarily store data being operated;and a file device to store the signal processing program, samplingfunctions, and the like. The signal processing program provides theprocedure for a computer to execute each processing shown in FIG. 23.The signal processing program is available as an independent programthat is stored on recording media such as CD-ROM.

When one type of parameter m is available, there are available one innerproduct operating unit 4 and one sampling function generator 3 in FIG.23. The error operating unit 7 is omitted. The class judging unit 8outputs a corresponding fixed parameter m signal.

The signal processing device according to the embodiment can also use ananalog signal processing to generate a discrete signal from a continuouswaveform signal. FIG. 24 shows the construction of the signal processingdevice using such analog signal processing. The device components arecomposed of analog circuits whose functions and operations are the sameas those of the corresponding components in FIG. 23. As an exception,the output circuit 9 outputs analog output signals. In this case, thesignals may be combined by inserting the parameter m signal into ablanking period of scanning for videos or images. A PCM coder can beused to previously encode and digitize discrete signals and theparameter m signal to be supplied to the output circuit 9. In this case,the output circuit 9 in FIG. 23 is used to output digital outputsignals.

According to the embodiment, the inner product operating unit 4 outputsan inner product operating value for parameter m determined by the classjudging unit 8. Since that parameter m matches parameter m of the inputsignal, the output inner product operating value approximately matchesthe sampling value of the sampling circuit 2. Accordingly, the innerproduct operating value can replace the sampling value to be supplied tothe output circuit 9. In this case, a selector is provided to select aninner product operating value for the determined parameter m using theparameter m signal output from the class judging unit 8 and supply theoutput circuit 9 with the selected inner product operating value. FIG.25 shows the construction that provides the selector. In FIG. 25,reference numeral 10 denotes the selector. In this manner, the signalprocessing device in FIG. 25 outputs a discrete signal composed of astring of inner product operating values. As mentioned above, the signalprocessing device in FIG. 23 outputs a discrete signal composed of astring of sampling values. Each of the inner product operating value andthe sampling value is discrete values acquired at every samplinginterval. Therefore, the discrete signal can be referred to as adiscrete value string.

The following items may be also applicable to the principle ofoperations and processing flows of the signal processing deviceaccording to the ninth and tenth embodiments.

<I> Determining an Optimum Class for an Unknown Signal in a PartialSpace of the Fluency Signal Space

(1) Defining the Fluency Signal Space

(2) Meaning of the Sampling Function

(3) Using the Sampling Function to Specify a Class of Partial SignalSpace to Which an Unknown Signal Belongs

However, these are the same as for the first through fourth embodimentsand a description is omitted for simplicity.

Further, description is omitted about the inner product operating units4 in FIGS. 22 and 23 constructed according to the above-mentioned theorybecause FIG. 9 shows the example of the inner product operating unit 4.

<II> Detecting a Changing Point

As mentioned above, the changing point includes a class switching pointand a peculiar point.

(1) Class Switching Point

Let us suppose that a signal is represented by a string of signals withdifferent classes. Such signal contains a point (class switching point)as a boundary between signals with different classes. The classswitching point is detected based on a difference between an innerproduct operating value and an input signal's sampling value. The innerproduct operating value results from taking an inner product between thesampling function system and the original signal (input signal).

With reference to a point along a signal, the original signal may berepresented by signals with different classes in the domains before andafter that point. For example, the signal is represented as signal

^(m) ^(A) S

in domain A. The signal is represented as signal

^(m) ^(B) S

in domain B. The point separates domains based on the signals withdifferent classes and is referred to as a class switching pointrepresented by P(m_(A), m_(B)).

The class switching point P(m_(A), m_(B)) is classified as followsdepending on properties at the point.

(i) The point P(m_(A), m_(B)) makes the signal continuous butundifferentiatable and satisfies the condition m_(A)≠m_(B). FIG. 26exemplifies such class switching point.

(ii) The point P(m_(A), m_(B)) makes the signal discontinuous and istherefore undifferentiatable and satisfies the condition m_(A)≠m_(B).FIG. 27 exemplifies such class switching point.

(iii) The point P(m_(A), m_(B)) makes the signal continuous anddifferentiatable and satisfies the condition m_(A)≠M_(B). FIG. 28exemplifies such class switching point.

(2) Peculiar Point

A point, referred to as a peculiar point, undifferentiatably divides thedomain into domains A and B. According to its properties, the peculiarpoint is classified as follows.

(i) The point makes the signal continuous but undifferentiatable andsatisfies the condition m_(A)=m_(B). FIG. 29 exemplifies such peculiarpoint. Especially, when m_(A)=m_(B)=2 is satisfied, for example, thepeculiar point becomes a polygonal line's joining.

(ii) The point makes the signal discontinuous and is thereforeundifferentiatable and satisfies the condition m_(A)=m_(B). FIG. 31exemplifies such peculiar point.

(iii) The point makes the signal continuous or discontinuous and istherefore undifferentiatable and satisfies the condition m_(A)≠m_(B).Such peculiar point is the same as the class switching points (i) and(ii). Among class switching points, such peculiar point is referred toas an ultra peculiar point.

(3) Detecting the Changing Point

The ninth and tenth embodiments provide a difference between thesampling value and the inner product operating value. The differencebecomes a small value (approximately 0) at a position short of thechanging point containing the above-mentioned class switching point andthe peculiar point because m matches parameter m_(A). The differencebecomes a large value because m differs from the other parameters m. Thechanging point provides a boundary where the differentiation isimpossible or parameter m changes drastically. The difference valuebecomes large with reference to parameter m_(A). In consideration forthis, specified threshold value ε_(th) is provided. Differences for allparameters m may exceed threshold value ε_(th) at a point. This pointcan be determined to be the changing point.

FIG. 32 provides an example of detecting such changing point. As shownin FIG. 32, let us suppose that signal u(t) is represented as a classm=2 signal (polygonal line) in a given span (domain A). In addition, letus suppose that signal u(t) is represented as a class m=∞ signal inanother span (domain B) at t=t_(sp) and later. Moreover, the signal isassumed to belong to a m=3 class.

(i) In domain A, an inner product operating value results from an innerproduct between sampling function

_([AD]) ^(m) ⁰ ψ(t)

for class m₀ and signal u(t). There is a difference (expressed as

_(m) ₀ ε(A)

corresponding to domain A) between the inner product operating value andthe input signal's sampling value. The errors are calculated withrespect to m₀=2, 3, and ∞ to result in errors ₂ε(A), ₃ε(A), and_(∞)ε(A). Of these errors, ₂ε(A) becomes the minimum.

(ii) Similarly, errors ₂ε(B), ₃ε(B), and _(∞)ε(B) are found in domain B.Of these, _(∞)ε(B) becomes the minimum in this domain.

(iii) Errors ₂ε(t_(sp)), ₃ε(t_(sp)), and _(∞)ε(t_(sp)) are found in thevicinity of ultra peculiar point t=t_(sp) where the class changes.Values ₂ε, ₃ε, and _(∞)ε, all become large, making it difficult toclearly specify a class. Based on this information, the class switchingpoint is positioned.

With reference to FIG. 33, the following describes a class determinationprocessing based on the above-mentioned principle. As mentioned above,the description concerns the example where the sampling function isapplicable to the classes m₀=2, 3, and ∞.

At each of sampling points t_(k), t_(k+1), . . . , and t_(k+(J−2)), theprocessing takes an inner product between input signal u(t) and thesampling function

_([AD]) ^(m) ⁰ ψ(t)

to find an inner product operating value

^(m) ⁰ û(t_(k))

where k=k, k+1, . . . , and k+(J−2). The processing then calculates anerror

_(m) ₀ ε(t_(k))

between the calculated inner product operating value and the samplingvalue u(t_(k)) for the input signal (Step S8). So far, the processing isthe same as that at Steps S1 through S5 in FIG. 8 based on m₀=2, 3, and∞.

The processing compares errors ₂ε(t_(k)), ₃ε(t_(k)), and _(∞)ε(t_(k))corresponding to each m0 with predetermined threshold value ε_(th) (StepS9). When all errors are greater than or equal to threshold value ε_(th)(Step S10), the processing assumes the point corresponding to t=t_(k) tobe a changing point (Step S11). At Step S10, there may be a case whereall errors are not greater than or equal to threshold value ε_(th) andat least one error is smaller than or equal to ε_(th). In this case, theprocessing returns to Step S9.

According to the ninth and tenth embodiments as mentioned above, aninner product operation can be used to find changing points on anoutline. The inner product operation contains the integration.Differently from the changing point detection using the differentiationas has been practiced so far, it is expected to decrease effects ofnoise during the changing point detection and reliably acquire highlyaccurate changing points.

In addition, the tenth embodiment clarifies the class belonging to theinput signal to be processed during the signal processing to acquire adiscrete signal from the input signal as the continuous waveform signal.It is expected to acquire parameter m signals indicating classes andchanging point signals indicating changing points as well as discretesignals.

During the signal processing to generate a continuous waveform signalfrom a discrete signal, the parameter m signal and the changing pointsignal can be used to select the inverse sampling function correspondingto the parameter m. In this manner, it is possible to generate thecontinuous waveform signal using the inverse sampling function withparameter m matching the parameter m to which the discrete signalbelongs. Consequently, it is possible to reproduce high-qualitycontinuous waveform signals independently of band limitations accordingto the Shannon's sampling theorem.

To be more specific, the following describes a device for generating acontinuous waveform signal from a discrete signal. FIG. 34 shows theconfiguration of the device. A signal supplied to the device isequivalent to a digital signal output from the signal processing deviceaccording to the ninth embodiment. The digital signal processing isperformed to acquire the continuous waveform signal from a discretesignal.

The inverse sampling function used for the signal processing isbiorthogonal to the above-mentioned sampling function that is used forthe signal processing device according to the ninth embodiment. Theinverse sampling function with m=2 and 3 is settled within the finitespan to (P−1)τ. The convoluting integration is performed at eachsampling point within this span. When m is 3, P is typically set to 5.The inverse sampling function with m=∞ infinitely continues oscillation.Accordingly, the device limits the span for this function to the samespan for the function with m=2 or 3. A resulting slight error isallowable. To increase the processing accuracy for m=∞, the range ofconvolution integration can be wider than the above-mentioned one.

In FIG. 34, reference numeral 21 denotes a signal input circuit that issupplied with a digital signal composed of a discrete signal as anoriginal signal belonging to parameter m, a parameter m signalindicating the parameter m, and a changing point signal, and separatesthese signals from each other and outputs them; 22 denotes an inversesampling function generator that generates an inverse sampling functionfor each of parameters m; 23 denotes an inverse sampling functionselector that uses the parameter m signal and the changing point signalto select an inverse sampling function with parameter m corresponding tothe discrete signal out of inverse sampling functions with each ofparameter m output from the inverse sampling function generator 22; 24denotes a convoluting integrator that acquires a continuous waveformsignal by performing convolution integration between the discrete signalfrom the signal input circuit 21 and the inverse sampling functionselected by the inverse sampling function selector 23; and 25 denotes aPCM decoder (PCMDEC) that outputs an analog signal equivalent to thecontinuous waveform signal output from the convoluting integrator 24.The inverse sampling functions for m=2, 3, and ∞ output from the inversesampling function generator 22 are previously stored in a data file (notshown) of a storage device and are read each time a function isselected.

The PCM decoder 25 is unnecessary when output signals from the signalprocessing device in FIG. 34 are supplied to a digital-input device(e.g., printer). FIG. 35 shows the configuration of the device thatomits the PCM decoder 25 and outputs digital continuous waveformsignals.

As mentioned above, the inverse sampling function with parameter m isexpressed as follows.

_([DA]) ^(m)ψ(t)

Further, as mentioned above, the inverse sampling function and thesampling function are associated with each other so as to bebiorthogonal. In particular, the inverse sampling function is configuredto be set to a given value at a targeted sampling point and reset to 0at the other sampling points.

Equation (13) above expresses the convolution integration for DAoperations. Operating equation (13) can yield continuous waveform signalu(t) that reproduces the original signal. Accordingly, a sampling valuefor sampling point t_(k) is held for (P−1)τfrom t=t_(k). The held signalis multiplied by the inverse sampling function that starts beinggenerated from t=t_(k). The operation is performed as often as (P−2)times at a sampling interval of τ. The resulting products are addedaccumulatively in succession. The same operation is repeated from thenext sampling point t_(k+(P−1)) to operate the convolution integrationand acquire continuous waveform signal u(t). As mentioned above, suchprocessing to acquire a continuous waveform signal from discrete signalssmoothly connects between discrete values using the DA function (inversesampling function) with parameter m. The processing can be defined as aninterpolation or a processing treatment to acquire a continuous signal.

In consideration for this, for example, the convoluting integrator 24 inFIG. 34 can be constructed as shown in FIG. 16. That is, the convolutingintegrator 24 is composed of: delay circuits 51-1 through 51-(P−2) asmany as (P−2) to delay the inverse sampling function by τ; holdingcircuits 52-0 through 52-(P−2) as many as (P−1) to hold sampling valuesfor sampling points t_(k), t_(k+1), . . . , and t_(k+(P−2)) at intervalτ; multipliers 53-0 through 53-(P−2) as many as (P−1) to multiply aholding signal output from the holding circuit 52 by the inversesampling function; and an accumulator 54 to accumulatively add outputsignals from the multiplier 53 in the order of output.

As mentioned above, the embodiment enables the signal processing usingthe inverse sampling functions appropriate to classes, making itpossible to acquire high-quality reproduction signals.

According to the tenth embodiment, the signal processing devices inFIGS. 23 and 25 and the signal processing device provided with the PCMcoder at the output side in FIG. 24 are supplied with analog continuouswaveform signals and output digital discrete signals (discrete valuestrings). Therefore, the above signal processing devices can beinterpreted as an AD converter. Similarly, the signal processing devicesin FIGS. 34 and 35 can be interpreted as DA converters. When bothdevices construct an A-D/D-A conversion system, both devices may bedirectly connected or may be connected via a transmission system or arecording system. When data passes through the transmission system orthe recording system, information compression coding or transmissionpath coding may be provided to decrease the amount of data. In thiscase, data passes through the transmission system or the recordingsystem, and then is decoded and D-A converted.

When the transmission system is a communication system, it is availableas Internet, cellular phone networks, and cable television, orground-based broadcasting and satellite broadcasting using radio waves.The recording system can provide recording media such as CD (CompactDisc) and DVD (Digital Versatile Disc). Through the use of thesetechnologies, it is expected to provide higher-precision image than everbefore.

When the A-D/D-A conversion system is applied to a signboard productionsystem, a print system, and the like, the system can provide muchhigher-precision images than ever before. Even when an image is enlargedor reduced, it is expected to maintain high quality, that is, providehigh scalability.

INDUSTRIAL APPLICABILITY

The invention can be widely applied to information industries in generalrelated to image, video, data, audio, and the like, i.e., recordingmedia, internet, computers, printing, publishing, advertisement, and thelike.

1. A signal processing method comprising the steps of: providing aplurality of fluency digital/analog (D/A) functions classified withparameters m; inputting a predetermined parameter m and discrete signalvalues; selecting a fluency D/A function from the plurality of fluencyD/A functions according to the predetermined parameter m; and generatinga continuous signal by performing convoluting integration between theselected fluency D/A function and the inputted discrete signal values.2. The signal processing method according to claim 1, wherein theparameter m is a parameter denoting that the fluency D/A function of theparameter m is continuously differentiable only as often as (m−2) times,and wherein the parameters m contain at least three types which are m=2,3, and ∞.
 3. The signal processing method according to claim 1, whereinthe predetermined parameter m and the discrete signal values areinputted through a recording medium or a communication means.
 4. Thesignal processing method according to any one of claims 1, 2 or 3,wherein the continuous signal is a signal gotten through digital signalprocessing.
 5. A signal processing device comprising: a plurality offluency D/A functions which provides a plurality of fluency D/Afunctions classified with parameters m; an input device which inputs apredetermined parameter m and discrete signal values; an operating unitwhich outputs a continuous signal by performing convoluting integrationbetween a fluency D/A function selected from the plurality of fluencyD/A functions and the discrete signal values.
 6. A signal processingmethod comprising the steps of: inputting a discrete signal and a signalindicating a parameter m; converting the discrete signal into acontinuous signal in a fluency signal space of the parameter m.